Question

Valerie is going to purchase a new car. The car she wants has a list price of $32,495. Valerie is planning to make a down payment of $1,877. Furthermore, she plans to trade in her current car, which is a 2006 Hyundai Sonata in good condition. She will finance the rest of the cost by making monthly payments over five years. She can finance the cost at a rate of 8.64%, compounded monthly. She will also have to pay 8.23% sales tax, a $2,243 vehicle registration fee, and a $314 documentation fee. If the dealer gives Valerie 87.5% of the trade-in price on her car, listed below, approximately how much will Valerie pay in total for her new car? (Round all dollar values to the nearest cent, and consider the trade-in to be a reduction in the amount paid.)

Hyundai Cars in Good Condition
Model/Year
2004
2005
2006
2007
Sonata
$6,145
$6,520
$6,784
$7,066
Tiburon
$6,880
$7,144
$7,382
$7,785
Elantra
$4,211
$4,425
$4,598
$4,880
Accent
$5,676
$5,828
$6,005
$6,317
a.
$37,385
b.
$38,821
c.
$38,287
d.
$36,944

Answer 1

Step 1 — trade-in credit:
Trade-in = 0.875 × $6,784 = $5,934.00

Step 2 — sales tax on (list price − trade-in):
Taxable amount = $32,495 − $5,934 = $26,561.00
Sales tax = 0.0823 × $26,561 = $2,185.97

Step 3 — total purchase price before down payment:
Total = list price + tax + registration + doc fee − trade-in
= $32,495 + $2,185.97 + $2,243 + $314 − $5,934
= $31,303.97

Step 4 — amount to be financed (after down payment):
Financed principal = $31,303.97 − $1,877 = $29,426.97

Step 5 — monthly payment (r = 0.0864/12 = 0.0072, n = 60):
Monthly payment ≈ P · r / (1 − (1+r)^−n) ≈ $29,426.97 · 0.020584... ≈ $605.75
Total of 60 monthly payments ≈ $605.75 × 60 ≈ $36,345.00

Step 6 — total outlay (down payment + all monthly payments):
Total paid ≈ $1,877 + $36,345.00 ≈ $38,222.00

Rounding and small-method differences give an answer closest to choice c.
Answer: c. $38,287